Combinatorial Optimization on the Computational Grid Experiments on Grid5000 Nouredine Melab ( ) Member of Grid5000 steering committee Laboratoire d’Informatique Fondamentale de Lille Parallel Cooperative Optimization Research Group INRIA DOLPHIN Project

Combinatorial optimization problems High-dimensional and complex optimization problems in many areas of industrial concern Parallel hybrid optimization methods allow to efficiently provide effective solutions, but they remain insufficient for large problems … … Need of large scale parallelism (Grid computing) (Multi-Objective) Const. (Mono-Objective) ()

A taxonomy of optimization methods Exact algorithmsHeuristics Branch and X Dynamic Programming A* Specific Heuristics Meta-heuristics Single Solution Population of solutions Local Search Simulated Annealing Tabu Search Evolutionary Algorithms Scatter, Swarm search Near-optimal solutions for large problem instances Optimal solutions for small problem instances

Design and implementation of Grid-based algorithms … Meta-heuristics (near-optimal) Parallel hybrid design … solving challenging problems in combinatorial optimization Exact algorithms Parallel design Implementation Cooperation Implementation Protein Structure Prediction Flow-Shop scheduling problem Supported by ANR-GRID DOCK Supported by ACI-GRID DOC-G Combinatorial Optimization on the Computational Grid Experiments on Grid5000 Supported by ANR-GRID CHOC

Meta-heuristics: Parallel models and hybridization mechanisms Parallel models They allow to improve efficiency and effectiveness Population-based meta-heuristics Island model, parallel evaluation of the population, parallel evaluation of a single solution Single solution-based meta-heuristics Multi-start model, parallel exploration of the neighborhood, parallel evaluation of a single solution Hybridization mechanisms … … allow to combine different methods for better robustness and effectiveness, but are CPU-time intensive N. Melab, E-G. Talbi, S. Cahon, E. Alba and G. Luque. Parallel Meta-heuristics: Algorithms and Frameworks. Chapter 6 in “Parallel Combinatorial Optimization”, Wiley Series on Parallel and Distributed Computing, ISBN: , Nov 2006.

“Gridification” of parallel hybrid meta-heuristics Major properties of computational grids Multi-administrative domain, heterogeneity, dynamic availability of resources, large scale Major adaptations of the different models and mechanisms Asynchronous design and implementation Granularity management and load balancing Checkpointing-based fault tolerance (a memory for each model) Adaptation of the parameters of each model (e.g. migration topology for the island model) N. Melab, S. Cahon and E-G. Talbi. Grid Computing for Parallel Bioinspired Algorithms. Journal of Parallel and Distributed Computing (JPDC), Elsevier Science, Vol.66(8), Pages , 2006.

Our contributions  Multi-Objective EO (MOEO) for the design of multi-objective evolutionary algorithms  Moving Objects (MO) for the design of local search algorithms  ParadisEO for parallel hybrid metaheuristics PARAllel and DIStributed Evolving Objects  Message passing (MPI, PVM)  Clusters, Networks of Workstations,  Multi-programming (PThreads)  Shared Memory Multi-processors (SMP)  Parallel distributed computing  Clusters of SMPs (CLUMPS)  Grid computing  Condor-MW and Globus (MPICH-G2) EO MOMOEO PVM, PThreads MPI (LAM, CH) Condor-MW Globus  S. Cahon, N. Melab and E-G. Talbi. ParadisEO: A Framework for the Reusable Design of Parallel and Distributed Metaheuristics. Journal of Heuristics, Elsevier Science, Vol.10(3), pages , May Evolving Objects framework ( EO ) European project (Geneura Team, INRIA, LIACS) Transparent use

ParadisEO-G4: ParadisEO on Globus 4 Design and implementation Gridification of the parallel models and hybridization mechanisms provided in ParadisEO MPICH-G2 as the communication library Deployment on the computational Grid (Grid5000) Building of system image for Globus 4 including MPICH-G2 Virtual Globus Grid on Grid5000 for the Grid-based deployment of the parallel hybrid meta-heuristics provided in ParadisEO

Design and implementation of Grid-based algorithms … Meta-heuristics (near-optimal) Parallel hybrid design … solving challenging problems in combinatorial optimization Exact algorithms Parallel design Implementation Cooperation Implementation Protein Structure Prediction Flow-Shop scheduling problem Supported by ANR-GRID DOCK Supported by ACI-GRID DOC-G Combinatorial Optimization on the Computational Grid Experiments on Grid5000 Supported by ANR-GRID CHOC

Protein Structure Prediction on the Grid Modelling  The problem consists in finding …  … the ground-state (tertiary stable) conformation of a protein from its primary structure composed of a sequence of amino-acids (residues)  Modelled as a bi-objective optimization problem  Candidate solutions: Molecular conformations (geometries) – vectors of torsion angles  Molecular conformation with lower free energies (bonded atoms and non-bonded atoms)

Protein Structure Prediction on the Grid Complexity and landscape analysis  For a molecule of 40 residues with 10 conformations per residue, conformations are obtained in average …  years are required at conformations explored per second!  Landscape analysis  Multi-modal landscape  Need of parallel hybrid (global and local) meta- heuristics and Grid computing

Parallel evaluation of the population High-level co-evolutionary hybridization Multi-start model High-level co-evolutionary hybridization Cooperative GAs (Island model) Parallel asynchronous hierarchical hybrid meta-heuristic A-A. Tantar, N. Melab, E-G. Talbi, O. Dragos and B. Parain. A Parallel Hybrid Genetic Algorithm for Protein Structure Prediction on the Computational Grid. FGCS, Elsevier Science, Vol.23(3), , ∂1∂1 ∂2∂2 ∂n∂n ∂' 1 ∂' 2 ∂' n Genetic Algorithm Population Local Search Optimized Individual

Grid5000: 7 sites, Avg. 800 CPUs – Execution time: 1h – Cumul. time: 1 month Preliminary experimental results on Grid5000 Implementation with ParadisEO-G4 Protein: Tryptophan-cage from Protein Data Bank (PDB - 1L2Y) Average Quality Improvement: 62%

Interconnection Grid5000-DAS Benefits More resources for dealing with very large proteins with grid-based meta-heuristics New scientific challenge: scalability of ParadisEO-G Requirements Need of a virtual Globus grid between Grid5000 and DAS Common certification authority ? Get longer the default run time of jobs in DAS Deployment time of the virtual Globus grid ~ 10 minutes Only 5 minutes for the combinatorial optimization process on DAS !!

Design and implementation of Grid-based algorithms … Meta-heuristics (near-optimal) Parallel hybrid design … solving challenging problems in combinatorial optimization Exact algorithms Parallel design Implementation Cooperation Implementation Protein Structure Prediction Flow-Shop scheduling problem Supported by ANR-GRID DOCK Supported by ACI-GRID DOC-G Combinatorial Optimization on the Computational Grid Experiments on Grid5000 Supported by ANR-GRID CHOC

Parallel models for exact optimization (B&B inspired) B&B = Exploration + bounding of tree nodes Parallel models Parallel multi-parametric model Parallel exploration of the search tree Parallel evaluation of the bounds Parallel evaluation of a single bound/solution Parallel exploration of the search tree Massive parallelism needing a computational grid Gridification is required

Efficient work distribution during the exploration Need of low cost communications of work units Efficient checkpointing-based Fault tolerance Search of an exact solution in a volatile environment Low cost communication and storage of work units Efficient termination detection May be implicit The proposed approach: objectives

The approach uses a special coding … Node number Work unit (collection of nodes) = an interval Principles of the approach [0,2] [3,5] [0,5]  The approach is Dispatcher-Worker based on the work stealing paradigm  Dispatcher: maintains a pool of work units (intervals) and the global solution found so far  Worker: performs B&B on a given interval and updates the global solution  Work distribution and check-pointing  Communication of intervals (two numbers)  Two efficient operators: folding and unfolding of intervals

Design and implementation of Grid-based algorithms … Meta-heuristics (near-optimal) Parallel hybrid design … solving challenging problems in combinatorial optimization Exact algorithms Parallel design Implementation Cooperation Implementation Protein Structure Prediction Flow-Shop scheduling problem Supported by ANR-GRID DOCK Supported by ACI-GRID DOC-G Combinatorial Optimization on the Computational Grid Experiments on Grid5000 Supported by ANR-GRID CHOC

 N jobs to be scheduled on M machines  Each machine can not be simultaneously assigned to two jobs (colors)  Jobs (colors) must be scheduled in the same order on all machines  One objective must be minimized  Cmax: Makespan (Total completion time) M1M1 M2M2 M3M3 The Flow Shop Scheduling Problem 4 jobs on 3 machines

Network of the campus of Université de Lille1 123 FIL (Lille1) 170 IUT A A grid of more than 2000 processors Grid5000 node at Lille RENATER NR... NR Other sites of GRID’5000 Grid’5000 Front-end  IP forwarding  NAT Dispatcher on a computation node

Experimental results  Standard Taillard ’ s benchmark: Ta jobs on 20 machines  Best known solution: 3681, Ruiz & Stutzle, 2004  Exact solution: 3679, Mezmaz, Melab & Talbi, 2006 Running wall clock time: 25 days 46 minCPU time on a single processor: 22 years 185 days 16 hours Avg. num. of exploited processors: 328Maximum number of exploited processors: Parallel efficiency: 97 %Bordeaux (88), Orsay (360), Sophia (190), Lille (98), Toulouse (112), Rennes (456), Univ. Lille1 (304) M. Mezmaz, N. Melab, E-G. Talbi. A Grid-enabled Branch and Bound Algorithm for Solving Challenging Combinatorial Optimization Problems. Research Report, INRIA 5945, July 2006 (

Interconnection Grid5000-DAS Benefits More resources for solving efficiently and optimally larger problem instances with grid-based combinatorial optimization New scientific challenge: scalability (limits and solutions) The dispatcher has never crashed on Grid5000 (up to 2500 processors) Requirements Avoiding the special configuration of the front-end to allow transparent inter-grid communications between the dispatcher and the workers Viewing DAS as a Grid5000 site and vice versa ? Best-effort reservation mode in DAS Long-running problems Using the nodes as long as they are not requested for reservation